Discussiones Mathematicae Differential Inclusions 19 (1999) 45-65

Andrea Gavioli

*Dipartimento di Matematica Pura e Applicata
Universita di Modena, via Campi 213/B, 41100 Modena, Italy*

We prove that the solutions of a sweeping process make up an R_{δ}-set
under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in
the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a
lipschitzian function, in such a way that the diameter of the neighbourhood and the
related Lipschitz constant do not depend on x and t. An application to the existence of
periodic solutions is given.

**Keywords:** nonconvex, sweeping process, wedged.

**1991 Mathematics Subject Classification:** 34A60, 34C25.

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Received 5 June 1999